Analytical solutions in R + qRn cosmology from singularity analysis

Abstract

The integrability of higher-order theories of gravity is of importance in the determining the proper-ties of these models and so their viability as models of reality. An important tool in the establishment of integrability is the singularity analysis. We apply this analysis to the case of fourth-order the-ory of gravity f(R) = R + qRn to establish those values of the free parameters q and n for which integrability in this sense exists. As a prelininary we examine the well-known case of n = 4/3.